Use of Monte Carlo Simulation in Remote Sensing

Data Analysis

Hamideh Ebrahimi, Student Member, IEEE, Shadi Aslebagh, Student Member, IEEE and Linwood Jones, Life Fellow, IEEE

Central Florida Remote Sensing Lab

Department of EECS

University of Central Florida

Orlando, FL 32816-2362

h_ebrahimi@knights.ucf.edu

Abstract— In the summer of 2011, the Aquarius earth science

satellite was launched to measure Sea Surface Salinity (SSS)

using a L-band microwave radiometer/scatterometer. This is an

important oceanic parameter for monitoring the earth’s water

cycle over oceans and for modeling global climate change. The

microwave remote sensing of SSS is a challenging objective. The

SSS signal is weak and there are many interfering error sources

that must be corrected to achieve an accurate SSS measurement.

This paper deals with the use of random processes theory for

assessing the effects of rainfall on the retrieved SSS.

In this paper we use the Monte Carlo method that is one of the

best methods for analysis of random processes, to investigate the

multilayer effect caused by rainfall on the L-band brightness

temperature and the resulting SSS retrieval.

Keywords—Monte Carlo simulation; Sea Surface Salinity;

multilayer media effect, ocean brightness temperature

I. INTRODUCTION

Earth climate scientists use earth remote sensing satellites to find patterns of climate changes by obtaining long time series of oceanic and atmospheric environmental parameters. For the ocean, these parameters include sea surface temperature, ocean surface wind speed and ocean color. Recently NASA acquired the ability to measure global salinity, which is the subject of this paper.

For this purpose, an L-band microwave radiometer/scatterometer (radar) named Aquarius (AQ) has been designed to map the surface salinity field of the oceans from space. It was launched into polar orbit on the Aquarius/SAC-D mission, which is a partnership between National Aeronautics and Space Administration (NASA) and the Comision Nacional de Actividades Espaciales (CONAE), Argentina Space Agency [1].

AQ provides monthly global maps of SSS measurements with high spatial (150 km) resolution and a precision of 0.2 practical salinity units (psu), which is equivalent of 1/8 teaspoon of salt dissolved in a gallon of water. One psu corresponds to measuring changes in the ocean surface brightness temperature (Tb) to a precision of about 0.1 Kelvin [2].

To retrieve SSS, AQ must measure the smooth ocean brightness temperature. Unfortunately, at the satellite, the antenna brightness temperature has contributions from a number of sources that must be estimated and removed before SSS can be retrieved. These include Tb’s from: the atmosphere, the galaxy and sun emissions, ocean roughness emissions due to winds and waves, and the emissions from rain.

Of these error sources, rain is one of the most difficult to correct. This is because rain is heterogeneous in space and transient in time and there are no independent rain measurements that are simultaneous and spatially collocated with the AQ Tb measurements.

Further, rainfall can affects the Tb measurement in two different ways. The first, called the “splash effect”, occurs during the rainfall, when the rain-drops hit the sea surface and make small-scale roughness that “warms the Tb”. The degree of warming depends upon the magnitude of rainfall (rain rate mm/hr) that is an exponential probability distribution function. The second, known as the “multilayer effect”, is caused by a layer of fresh water floating on the salty sea surface. This effect can either increase or decrease the Tb depending upon the thickness of the rain layer. Unfortunately this rain layer thickness is a random variable with a uniform probability distribution function (pdf).

Thus, the focus of this paper is to investigate this multilayer effect. We use electromagnetic (EM) theory to calculate the emissivity of a rain (fresh water) layer (with assumed random thickness) over a semi-infinite sea water medium. This is implemented using the Monte Carlo simulation method for calculating the ocean Tb and then analyzing the histograms of possible Tb’s.

II. BRIGHTNESS TEMPERATURE

To reduce the complexity of our analysis, we neglect the minor effect of galaxy and sun emissions contributions and examine the major sources of the measured brightness temperature as illustrated in figure 1. The measured antenna temperature is the combination of three different temperatures; Upwelling atmospheric brightness temperature, the downwelling atmospheric brightness temperature reflected

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upward at sea surface and the brightness temperature due to sea surface emission. At the AQ L-band frequency, the surface emission is dominant, and for simplicity only this will be considered in this paper.

For the ocean surface emission, there are a few parameters that affect the ocean Tb, namely; sea surface temperature (SST), ocean wind speed (WS), SSS and rain rate. The first two parameters are known as a priori information from numerical weather models and the SSS is the unknown parameter to be solved. Only the delta-Tb due to rain rate is an unknown random variable, which will be varied parametrically and the effect on ocean Tb determined from the Monte Carlo simulation. This analysis is capable of being performed at any antenna line-of-sight viewing (incidence angle), but for simplicity only the nadir viewing antenna geometry will be presented.

Figure 1. Components of the brightness temperature captured by the satellite

antenna.

III. MULTILAYER MEDIA

The intensity of an EM field decreases as it propagates into

a medium of finite conductivity (semiconductor). The depth of penetration (known as skin depth) is the distance whereby the electric field strength is reduced by a factor of (1/e) and is

√(

) √

√

(1)

Where is conductivity (S/m), is free space permeability and in our scenario f = 1.4 GHz. For sea water at

T = 25 C and SSS = 34 psu, conductivity is equal to

,

so the skin depth is 5.84 𝑚𝑚. However, for fresh water

So the skin depth is 13.5 c𝑚 < 𝑠𝑘𝑖𝑛 𝑑𝑒𝑝𝑡ℎ < 4.25 𝑚. Thus, we can assume that the fresh water layer is lossless for the expected depths of less than a few cm.

For normal incidence plane waves, the free space reflection and transmission at a semi-infinite air/ocean boundary is governed by the Fresnel voltage reflection coefficient that is the complex ratio of the reflected electric field to the incident field, and for two layers scenario we have

(2)

That and are the intrinsic impedances of the medium1 and medium2. Given the voltage reflection coefficient, the ocean blackbody emissivity is

ϵ= ( − 2)

And we define the ocean brightness temperature

For our case, medium-1 is air so the intrinsic impedances of it is equal to 377 and medium-2 is the ocean, which for our scenario with frequency = 1.4 GHz, SST = 25 C and SSS = 34 psu, 34.82 + 14.57i. The corresponding ocean brightness temperature is Tb = 92 K

In the presence of rainfall, we can have three layers (air, fresh water and ocean water), as shown in Figure 2, and in this scenario the reflection coefficient is

(3)

Where is the equivalent intrinsic impedance for medium-2 and -3 combined (as a single equivalent layer), which equals

[ ( ) ( )

( ) ( )] (4)

Where L is equal to the thickness of the fresh water layer

caused by rain, and 𝑘 is equal to 𝑘 √ , where is

the permittivity of medium-2 (fresh water layer) and is the permeability of space respectively, and is the angular frequency of the wave [3].

Figure 2. Three Layers Media

As the thickness of the fresh water layer varies, the Fresnel voltage reflection coefficient and the corresponding ocean Tb oscillates with a period of half of a wavelength in the fresh water medium as shown in Fig. 3. When the layer thickness = 0 (or a multiply of half of wavelength), the Tb is equal to the two-layer case (no rain). In this figure, this is indicated by a dashed red line.

Ocean

Surface

Emission

Upwelling

Brightness

Reflected

Brightness Down-welling

Brightness

Atmospheric

Emission

Satellite Antenna

Medium1: air ŋ1

Medium2: Sea water ŋ3

Medium2: Fresh water ŋ

2 L: Thickness

Figure 3. Brightness temperature of fresh-water layer over sea water.

Since, the ocean Tb repeats every half-wavelength, the Monte Carlo simulation the unknown thickness as a uniformly distributed random variable (equally likely) between zero and one half-wavelength.

IV. SIMULATION AND RESULTS

For the simulation of the multilayer effect of the rainfall, we used the Monte Carlo method with repetitively of 10,000 trials for each rain case [4]. We assumed an ideal flat ocean surface that the thickness of the fresh water layer is a uniform random function between zero and one half-wavelength. The EM wave emission is perpendicular to the surface (nadir

antenna viewing). We assume that the antenna field of view (antenna footprint) corresponds to 10,000 pixels, where we calculated the Monte Carlo brightness temperature for variable rain beam-fill fraction defined as (#rainy pixels/10,000). Further, we varied the beam-fill fraction from 1% to 25%.

In Fig. 4, the histograms of the measured (antenna footprint average) brightness temperature for different rain beam-fill fractions are shown. As resulting histograms appear to be Gaussian distributed, and the corresponding “best fit” Gaussian functions are plotted with red color.

The results of the mean and standard deviation of rain induced excess ocean are shown in the Fig. 5. The red star-symbol presents the change in ocean Tb from the no-rain case. We calculate this as the difference between the histogram mean and the rain-free ocean Tb.

V. CONCLUSION

Sea surface salinity is an important parameter in the modeling the climate changes and there are several environmental parameters that cause error in measuring this parameter, that rainfall is one of them, in this paper using the Monte Carlo method, we investigated the multilayer effect caused by rainfall.

We measured the average value and standard deviation of this footprint average Tb as a function of rain-fill fraction. These data will be used in further analysis to determine the effect of rain contamination on the retrieval of SSS.

0 0.005 0.01 0.015 0.02 0.025 0.0370

80

90

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160

Fresh Water Layer Thickness (m)

Brightn

ess T

em

pera

ture

(K

)

Tb vs Fresh water Thickness

Lambda/2

92.8 92.85 92.9 92.95 93 93.050

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700hist of average Tb for 1% rainy part

Temperature (K)

# o

f occura

nce

93.2 93.3 93.4 93.5 93.6 93.7 93.80

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700hist of average Tb for 5% rainy part

Temperature (K)

# o

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93.9 94 94.1 94.2 94.3 94.4 94.5 94.60

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700hist of average Tb for 10% rainy part

Temperature (K)

# o

f occura

nce

94.4 94.6 94.8 95 95.2 95.40

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700hist of average Tb for 15% rainy part

Temperature (K)

# o

f occura

nce

95.2 95.4 95.6 95.8 96 96.20

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700hist of average Tb for 20% rainy part

Temperature (K)

# o

f occura

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95.8 96 96.2 96.4 96.6 96.8 97 97.20

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500

600

700hist of average Tb for 25% rainy part

Temperature (K)

# o

f occura

nce

Figure 4. The histogram of average brightness temperature for 1, 5, 10, 15, 20 and 25% rain beam-fill fraction.

Figure 5. Mean and STD of the Tb for different Rain percentage

ACKNOWLEDGMENT

This research at CFRSL was performed under a grant with NASA Headquarter Earth Science Program.

REFERENCES

[1] Le Vine, D.M.; Lagerloef, G.S.E.; Colomb, F.R.; Yueh, S.H.; Pellerano,

F.A.; , "Aquarius: An Instrument to Monitor Sea Surface Salinity From Space," Geoscience and Remote Sensing, IEEE Transactions on , vol.45, no.7, pp.2040-2050, July 2007

[2] Le Vine, D.M.; Lagerloef, G.S.E.; Torrusio, S.E.; , "Aquarius and Remote Sensing of Sea Surface Salinity from Space," Proceedings of the IEEE , vol.98, no.5, pp.688-703, May 2010

[3] Cheng, D. K. Field and wave electromagnetics / David K. Cheng. Reading, Mass. : Addison Wesley, 1985, c1983.

[4] D.P. Kroese, T. Taimre, Z.I. Botev . Handbook of Monte Carlo Methods, Wiley Series in Probability and Statistics, John Wiley and Sons, New York, 2011

0 5 10 15 20 250

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4Mean & STD for extra Tb for different rain percentage

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